The use of quantum mechanics in the treatment of waveguides

William Konyk, Julio R. Gea-Banacloche

Tomio Yamakoshi Petrosky, Yuki Goto, Savannah Sterling Garmon

In this paper, we review a new treatment of classical radiation damping, which resolves a well-known contradiction in the Abraham-Lorentz equation that has long been a concern. This radiation damping problem has already been solved in quantum mechanics by the method introduced by Friedrichs. Based on Friedrichs’ treatment, we solved this long-standing problem by classicizing quantum mechanics by replacing the canonical commutation relation in quantum mechanics with the Poisson bracket relation in classical mechanics. As an application of our new approach, we will analyze the anomalous damping experienced by electrons undergoing cyclotron motion inside a waveguide near the cut-off frequency. This anomalous damping cannot be described using the existing Abraham-Lorentz equation.

Fatih Dinç, İlke Ercan

In this paper, we provide a rigorous quantum mechanical derivation for the coherent photon transport characteristics of a two-level atom coupled to a waveguide without linearizing the coupling coefficient between the light and the atom. We propose a novel single frequency sampling method that allows us to treat the singularities in real space scattering potential despite the non-convergence property. We also study the conditions under which the linearization of the coupling coefficient is an accurate assumption. This allows us to confirm and expand on the findings of the existing literature while obtaining the dynamic electronic polarizability for the two-level atom confined to a 1-D waveguide while using an interaction Hamiltonian with rotating-wave approximation.

Jingbo Wang

Jung‐Tsung Shen, Shanhui Fan

We analyze the single-photon transport in a single-mode waveguide coupled to a whispering-gallery-type resonator interacting with a two-level atom. The single-photon transport properties such as the transmission and reflection amplitudes, as well as the resonator and the atom responses, are solved exactly via a real-space approach. The treatment includes the inter-mode backscattering between the two degenerate whispering gallery modes of the resonator, and the dissipations of the resonator and the atom. We also show that a generalized critical coupling condition, that the single-photon transmission at the output of the waveguide goes to zero on resonance for a matched system, holds for the full coupled waveguide-ring resonator-atom system.